Viewing

• This is chapter 5 of the book.
• Viewing is the process of transforming 3D objects onto a fixed 2D screen.
• Viewing is almost completely accomplished by matrix - matrix and matrix vector multiplications.
• This is the real applied linear algebra chapter.
• Typically
  • Models are created in their own coordinate system. The modeling coordinate system
  • Models are combined into a world coordinate system
  • This is usually viewed from a camera coordinate system
  • Which is transformed to NDC to DC by the process we have seen.
  • 
• When building a scene
  • Move the models to the proper location in world coordinates.
    • This is normally done with scales, rotates and translate.
  • Place the camera in world coordinates
  • Transform the entire scene to camera coordinates.
  • Apply a lens transformation
• We normally work in homogeneous coordinate systems.
  • More on this later, but for now, (x,y,z,1)
• Most camera transformations imply a view frustum
  • The basic model is a pinhole-camera
  • Along with a near plane and a far plane.
  • The goal is to project items in the view volume onto the near plane.
  • 
  • As rays shoot off into the distance, the view frustum is created.
  • The near plane is used to throw away items too close to the viewer
  • The far plane is used to eliminate objects too far in the distance to be seen.
  • A prospective projection can be employed to map this strange shape to the NDC cube.
    • This allows distant objects to appear smaller.
    • And parallel lines going into the distance merge.
  • At other times, in an orthographic projection, the z coordinate is just discarded.
    • And parallel lines remain parallel.
    • But there is no depth queue from prospective.